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Script is a kind of structured knowledge extracted from texts, which contains a sequence of events. Based on such knowledge, script event prediction aims to predict the subsequent event. To do so, two aspects should be considered for events, namely, event description (i.e., what the events should contain) and event encoding (i.e., how they should be encoded). Most existing methods describe an event by a verb together with only a few core arguments (i.e., subject, object, and indirect object), which are not precise. In addition, existing event encoders are limited to a fixed number of arguments, which are not flexible to deal with extra information. Thus, in this paper, we propose the Rich Event Prediction (REP) framework for script event prediction. Fundamentally, it is based on the proposed rich event description, which enriches the existing ones with three kinds of important information, namely, the senses of verbs, extra semantic roles, and types of participants. REP contains an event extractor to extract such information from texts. Based on the extracted rich information, a predictor then selects the most probable subsequent event. The core component of the predictor is a transformer-based event encoder to flexibly deal with an arbitrary number of arguments. Experimental results on the widely used Gigaword Corpus show the effectiveness of the proposed framework.